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04-BS-1: December 2018

Nivaar worked solution (AI-drafted; not reviewed by a licensed engineer)

  1. Question 1 General Solutions of Two First–/Second–Order ODEs
  2. Question 2 General Solution of a Doubly-Forced Oscillator (Resonant + Non-Resonant)
  3. Question 3 Constrained Extrema on an Ellipsoid (Lagrange Multipliers)
  4. Question 4 Two Lines in Space — Intersection, Orthogonal Line, Common Plane
  5. Question 5 Angle Between a Line and a Surface
  6. Question 6 Flux Through a Closed Surface (Divergence Theorem)
  7. Question 7 Work Done by a Conservative Field Along a Curved Path
  8. Question 8 Line Integral via Stokes' Theorem (Cylinder ∩ Plane)

Start with Question 1 →

National Exams — December 2018 — 04-BS-1 Mathematics. Three-hour, closed-book exam (one double-sided aid sheet permitted, approved calculator allowed). Format: eight questions offered; any five constitute a complete paper and only the first five appearing in the answer book are marked. All eight are solved below for completeness.

Reference texts: Kreyszig, Advanced Engineering Mathematics (10th ed., Wiley) — ODEs, forced oscillations, tangent planes, line/surface integrals, Stokes'/divergence theorems; Stewart, Calculus: Early Transcendentals (9th ed., Cengage) — vectors, gradients, constrained optimization.